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About the book

Description

This book, the second in a series of three on Convexity and Optimization, presents classical mathematical results for linear and convex optimization with an emphasis on the important concept of duality. Equivalent ways of formulating an optimization problem are presented, the Lagrange function and the dual problem are introduced, and conditions for strong duality are given. The general results are then specialized to the linear case, i.e. to linear programming, and the simplex algorithm is described in detail.

Content

Optimization

Optimization problems

Classification of optimization problems

Equivalent problem formulations

Some model examples

The Lagrange function

The Lagrange function and the dual problem

John’s theorem

Convex optimization

Strong duality

The Karush-Kuhn-Tucker theorem

The Lagrange multipliers

Linear programming

Optimal solutions

Duality

The simplex algorithm

Standard form

Informal description of the simplex algorithm

Basic solutions

The simplex algorithm

Bland’s anti cycling rule

Phase 1 of the simplex algorithm

Sensitivity analysis

The dual simplex algorithm

Complexity

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